Journal ArticleDOI
Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation
TLDR
In this paper, the authors consider finite time blow up solutions to the critical nonlinear Schrodinger equation, and prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L2 mass at the blow up point, the second part correspond to the regular part and has a strong L2 limit at blow up time.Abstract:
We consider finite time blow up solutions to the critical nonlinear Schrodinger equation Open image in new window For a suitable class of initial data in the energy space H1, we prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L2 mass at the blow up point, the second part corresponds to the regular part and has a strong L2 limit at blow up time.read more
Citations
More filters
Journal ArticleDOI
Asymptotics and blow-up for mass critical nonlinear dispersive equations
Frank Merle,Frank Merle +1 more
TL;DR: In this paper, the authors consider mass critical nonlinear Schrodinger and Korteweg-de Vries equations and present a review on results related to the blow-up of solution of these equations.
Dissertation
Etude qualitative de modèles dispersifs
TL;DR: In this paper, the authors consider the problem of Cauchy-Schrodinger L2-critique amortie in the regime log-log and the existence globale for the case of Ostrovsky-Burgers-I.
Posted Content
On a class of derivative Nonlinear Schr\"odinger-type equations in two spatial dimensions
TL;DR: In this paper, the authors present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions, which are of (derivative) nonlinear Schrodinger type and have recently been obtained in DLS for nonlinear optics.
Posted Content
Finite point blowup for the critical generalized Korteweg-de Vries equation.
Yvan Martel,Didier Pilod +1 more
TL;DR: In this paper, a single-bubble concentrating the ground state at a finite point with an unforeseen blow-up rate was shown to be possible for the Korteweg-de Vries equation.
Journal ArticleDOI
Rate of $L^2$-concentration of the blow-up solutionfor critical nonlinear Schrödinger equation with potential
TL;DR: In this article, the authors considered the blow-up solutions of the Cauchy problem for the critical nonlinear Schrodinger equation with a repulsive imbalance of harmonic potential.
References
More filters
Journal ArticleDOI
Nonlinear scalar field equations, I existence of a ground state
TL;DR: In this article, a constrained minimization method was proposed for the case of dimension N = 1 (Necessary and sufficient conditions) for the zero mass case, where N is the number of dimensions in the dimension N.
BookDOI
The nonlinear Schrödinger equation : self-focusing and wave collapse
TL;DR: In this article, the authors present a basic framework to understand structural properties and long-time behavior of standing wave solutions and their relationship to a mean field generation and acoustic wave coupling.
Journal ArticleDOI
On a class of nonlinear Schro¨dinger equations
TL;DR: In this paper, the existence of standing wave solutions of nonlinear Schrodinger equations was studied and sufficient conditions for nontrivial solutionsu ∈W¯¯¯¯1,2(ℝ�姫 n ) were established.
Journal ArticleDOI
Uniqueness of positive solutions of Δu−u+up=0 in Rn
TL;DR: In this article, the uniqueness of the positive, radially symmetric solution to the differential equation Δu−u+up=0 (with p>1) in a bounded or unbounded annular region in Rn for all n ≥ 1, with the Neumann boundary condition on the inner ball and the Dirichlet boundary condition decaying to zero in the case of an unbounded region, was established.
Journal ArticleDOI
Nonlinear Schrödinger equations and sharp interpolation estimates
TL;DR: In this paper, a sharp sufficient condition for global existence for the nonlinear Schrodinger equation is obtained for the case σ = 2/N. This condition is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of Nirenberg and Gagliardo.
Related Papers (5)
On universality of blow-up profile for L 2 critical nonlinear Schrödinger equation
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
Frank Merle,Pierre Raphaël +1 more